幂函数阻尼系统的振动特性分析

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振动与冲击 ›› 2025, Vol. 44 ›› Issue (4) : 91-97.

振动理论与交叉研究

幂函数阻尼系统的振动特性分析

杨晓彤1，申永军*2，张瑞良2

作者信息 +

Analysis of vibration characteristics of power function damping system

YANG Xiaotong1，SHEN Yongjun*2，ZHANG Ruiliang2

Author information +

文章历史 +

摘要

分析了含幂函数阻尼的单自由度系统在简谐激励下的受迫振动。通过平均法与等效线性化，推导了等效线性阻尼的表达式。研究发现，非线性阻尼的减振效果与其系数和指数密切相关。进一步得到了主系统振幅和相位的定常解，通过数值仿真验证了定常解的正确性。通过等效线性阻尼的变化曲线和幅频响应曲线，分析了影响非线性阻尼减振效果的因素。研究表明，阻尼比的增加会使共振峰值左移，提高了减振性能，但需在适当范围内控制阻尼比以实现最佳减振效果。此外，阻尼比较小时阻尼指数的增加能增强阻尼作用，但过大的阻尼比会导致非线性阻尼减振效果低于线性阻尼。本研究为结构减振设计及优化提供了重要依据和理论基础。

Abstract

The forced vibration of a single degree-of-freedom system with power function damping under simple harmonic excitation is analyzed. The expression of equivalent linear damping is derived by averaging method and equivalent linearization. It is found that the vibration reduction effect of nonlinear damping is closely related to its coefficient and exponent. The steady-state solution of the amplitude and phase of the main system is further obtained, and the correctness of the steady-state solution is verified by numerical simulation. The factors affecting the vibration reduction effect of nonlinear damping are analyzed by the changing curve of equivalent linear damping and the amplitude-frequency response curve. The study shows that the increase of damping ratio will shift the resonance peak to the left and improve the vibration reduction performance, but the damping ratio needs to be controlled within an appropriate range to achieve the best vibration reduction effect. In addition, when the damping ratio is small, the increase of damping index can enhance the damping effect, but too large damping ratio will cause the vibration reduction effect of nonlinear damping to be lower than that of linear damping. This results provide an important basis and theoretical foundation for structural vibration reduction design and optimization.

导出引用

杨晓彤1, 申永军2, 张瑞良2. 幂函数阻尼系统的振动特性分析[J]. 振动与冲击, 2025, 44(4): 91-97

YANG Xiaotong1, SHEN Yongjun2, ZHANG Ruiliang2. Analysis of vibration characteristics of power function damping system[J]. Journal of Vibration and Shock, 2025, 44(4): 91-97

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